4.6 Completing the Square

1,441 views

Published on

Published in: Technology
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
1,441
On SlideShare
0
From Embeds
0
Number of Embeds
29
Actions
Shares
0
Downloads
49
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

4.6 Completing the Square

  1. 1. 4.6 COMPLETING THE SQUARE
  2. 2. SOLVING BY FINDING SQUARE ROOTS <ul><li>Solving equations of the form </li></ul><ul><ul><li>Isolate the variable </li></ul></ul><ul><ul><li>“ Undo the Square” by taking the square root of both sides </li></ul></ul><ul><ul><li> Don’t forget: when you take the square </li></ul></ul><ul><ul><li> root your solution is ± </li></ul></ul>
  3. 3. EXAMPLE: SOLVE EACH EQUATION BY FINDING SQUARE ROOTS
  4. 4. EXAMPLE: SOLVE EACH EQUATION BY FINDING SQUARE ROOTS
  5. 5. EXAMPLE: SOLVE EACH EQUATION BY FINDING SQUARE ROOTS Note: No real number squared is equal to – 5, so the equation does not have a real number solution
  6. 6. SOLVING A PERFECT SQUARE TRINOMIAL <ul><li>Remember that a perfect square trinomials are of the form: </li></ul><ul><li>Sometimes they can be set equal to a constant </li></ul>
  7. 7. SOLVING A PERFECT SQUARE TRINOMIAL <ul><li>When a perfect square trinomial is set equal to a constant: </li></ul><ul><ul><li>Factor the trinomial </li></ul></ul><ul><ul><li>Take the square root of both sides </li></ul></ul><ul><ul><li>Solve for the value of the variable </li></ul></ul>
  8. 8. EXAMPLE: SOLVE EACH EQUATION
  9. 9. EXAMPLE: SOLVE EACH EQUATION
  10. 10. COMPLETING THE SQUARE <ul><li>If is part of a perfect square trinomial, we can find a constant c so that is a perfect square trinomial. </li></ul><ul><li>This is a process called completing the square </li></ul>
  11. 11. COMPLETING THE SQUARE <ul><li>We can form a perfect square trinomial </li></ul><ul><li> from by adding </li></ul>
  12. 12. COMPLETE THE SQUARE <ul><li>Find the value of </li></ul><ul><li>Add the value to the expression, this completes the square </li></ul>
  13. 13. EXAMPLE: COMPLETE THE SQUARE
  14. 14. EXAMPLE: COMPLETE THE SQUARE
  15. 15. SOLVING AN EQUATION BY COMPLETING THE SQUARE <ul><li>Rewrite the equation so it is of the form </li></ul><ul><li>Complete the Square: Add to both sides </li></ul><ul><li>Factor the prefect square trinomial </li></ul><ul><li>Take the square root of both sides </li></ul><ul><li>Solve for the variable </li></ul>
  16. 16. EXAMPLE: SOLVE EACH EQUATION BY COMPLETING THE SQUARE
  17. 17. EXAMPLE: SOLVE EACH EQUATION BY COMPLETING THE SQUARE
  18. 18. EXAMPLE: SOLVE EACH EQUATION BY COMPLETING THE SQUARE
  19. 19. HOMEWORK <ul><li>P 237 #1 – 8, 12 – 45 odd </li></ul>

×